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Stephen E Conrad Wolfram: Uma Trajetória De Contribuições Para a Tecnologia E a Matemática Magnus Cesar Ody Faculdades Integ

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Stephen E Conrad Wolfram: Uma Trajetória De Contribuições Para a Tecnologia E a Matemática Magnus Cesar Ody Faculdades Integ Stephen e Conrad Wolfram: uma trajetória de contribuições para a Tecnologia e a Matemática Magnus Cesar Ody Faculdades Integradas de Taquara - FACCAT [email protected] Lori Viali Pontifícia Universidade Católica do Rio Grande do Sul - PUCRS [email protected] Resumo: O artigo apresenta uma análise das contribuições dadas pelos irmãos Stephen Wolfram e Conrad Wolfram para os campos da Tecnologia e da Matemática. O objetivo é apresentar suas principais realizações nas pesquisas em tecnologia e apontar as relações com a Matemática e o seu ensino. Os dados foram coletados das informações disponíveis nos endereços wolfram.com, wolframalpha.com, computerbasedmath.org e conradwolfram.com. Identifica-se que juntamente em oferecer produtos e serviços de ponta para a computação, a pesquisa e o desenvolvimento científico em diferentes áreas, há a atenção para a matemática, tanto no seu ensino quanto na aprendizagem. Acreditam no ensino de matemática voltado para o uso do computador apoiando-se em metodologias adequadas que priorizem a resolução de problemas, a conceitualização e a reflexão. Palavras-chave: Uso do computador. Ensino de Matemática. Inovação. Pesquisa. Wolfram. 1. Introdução Pesquisas voltadas ao uso da tecnologia são relevantes, especialmente aquelas em prol da ciência da sociedade. Na maioria das vezes a tecnologia, quando criada, adapta-se naturalmente aos seus objetivos. Por exemplo, na medicina, quando um novo aparelho cirúrgico é criado, após testes, é inserido na prática hospitalar; ao lançar um novo modelo de celular, imediatamente os adeptos fazem uso. No caso do computador igualmente ocorre em todas as áreas. Mas o problema não é especialmente o computador enquanto máquina, mas seu efetivo uso, que nesse caso ainda é um problema para a educação (ODY, 2013) pela lacuna com relação ao uso efetivo na sociedade atual e especialmente na solução de problemas e sua utilização no contexto escolar e acadêmico. A Tecnologia e a Matemática resumem parte relevante das atividades desenvolvidas pelos Irmãos Stephen e Conrad Wolfram. A inovação e o espírito criativo fazem parte de suas trajetórias. Atualmente ambos são responsáveis pelo Wolfram Research, centro de pesquisas criado em 1987 com sedes em Illinois, Oxfordshire, Tóquio, Cambridge (MA) e Paris. Stephen é conhecido pelos Autômatos Celulares, pelos sistemas algébricos computacionais (SAC), sendo o mais lembrado o programa educacional Mathamática e pelo projeto Wolfran Alpha. Conrad por defender o uso do computador para ensinar matemática (computerbasedmath) e propor uma nova abordagem conceitual e metodológica. Nesse sentido, o artigo propõe discutir as contribuições dadas por Stephen Wolfram e Conrad Wolfram no campo da tecnologia da informação e da Matemática. Contudo, pretende- se analisá-las sob a ótica da educação e das ciências pelo fato dos irmãos terem atividades voltadas para diferentes áreas, mesmo o foco sendo a Matemática. Procura-se responder a seguinte pergunta: Quais contribuições de Stephen Wolfram e Conrad Wolfram são percebidas no campo da Tecnologia e da Matemática? Para isso o estudo possui abordagem qualitativa (DENZIN E LINCOLN, 2006) pela flexibilidade de analisar e compreender fenômenos sociais e humanos por meio da interpretação e da descrição de dados e eventos em que por vezes o pesquisador interage com o objeto de estudo. Os dados foram coletados das produções dos sujeitos da pesquisa e informações encontradas nos sítiosi disponíveis. 2. Stephen Wolfram Stephen Wolfram nasceu em Londres, Inglaterra, em 29 de agosto de 1959 (atualmente com 56 anos). Possui formação pelas universidades de Eton, Oxford e Caltech. Atua nas áreas da Matemática, Física (formação inicial) e Computação. O Doutorado, aos 20 anos, foi em Física Teórica pela Caltech, onde aos 21 anos passou a integrar o grupo docente (WOLFRAM, 2015). A Caltech é um Instituto de Tecnologia da Califórnia (California Institute of Tecnology) localizado na cidade Pasadena no estado da Califórnia, EUA. É considerada uma das melhores universidades do mundo onde atuam diversos condecorados com prêmios Nobel de inúmeras áreas. Dentre seus notáveis alunos podemos citar: Linus Pauling, Stanislav Konstantinovich Smirnov, Ronald W. Davis, William Alfred Fowler, Gregory Chamitoff, John McCarthy, etc. Desde sua fundação em 1891, tem atuado na formação profissional de seus alunos. Atualmente é referência mundial em pesquisas científicas com ênfase nas ciências naturais e na engenharia. Administra o laboratório de propulsão à jato (JPL) da NASA, o principal centro americano de exploração robótica. Dentre os objetivos do JPL está na contribuição das pesquisas sobre a origem do sistema solar, da própria atmosfera terrestre e missões com naves espaciais Três grandes projetos fazem parte da vida de Stephen Wolfram: o primeiro diz respeito ao Programa Computacional Mathematica, desenvolvido na década de 1980 com a finalidade de computar e resolver problemas nas mais diversas áreas do conhecimento. O segundo trata da escrita do livro A New Kind of Science fruto de suas pesquisas sobre autômatos celulares que, em suma, Stephen justifica pela frase […] a natureza usa regras simples para gerar a complexa realidade do mundo e todas podem ser computáveis (WOLFRAM, 2002). Originalmente os autômatos celulares foram estudados no final da década de 40 do século passado pelo matemático húngaro John Von Neumann e o matemático polaco Stanislaw Ulam, período em que o mundo da ciência computacional vivenciou fértil desenvolvimento de novas tecnologias. Consistiu em estudar técnicas computacionais a serem usadas para estabelecer modelos matemáticos que possam representar processos de crescimento e auto reprodução, Von Neumann (1966), Toffoli e Margulos (1987), Pascoal (2005). Um sistema com muitos elementos idênticos que interagem local e deterministicamente podem ser modelados usando autômatos celulares. De acordo com Melotti (2009, p. 7, grifo nosso), A ideia de autômatos celulares surgiu quando Stanislaw Ulam trabalhava no Laboratório Nacional de Los Alamos (Los Alamos, Novo México) estudou o crescimento de cristais, usando a mais simples rede (matriz) como seu modelo. Na mesma época Neumann trabalhava tendo como foco a auto reprodução. A ideia inicial era a capacidade de uma máquina se auto reproduzir e as cópias se auto reproduzirem, ou seja, cópias idênticas à máquina inicial. Ulam sugeriu que Von Neumann desenvolvesse o projeto dele em torno de uma abstração matemática, da mesma forma como Ulam usou para estudar o crescimento de cristais. Assim, nasceu o primeiro sistema de autômato celular de duas dimensões: a implementação de um algoritmo com a ideia de auto reprodução. De acordo com Gardner (1970) e Dewdney (1989) na década de 60 do século passado os autômatos celulares tiveram uma maior divulgação por meio do matemático Conway quando desenvolveu o jogo da vidaii. De acordo com Pascoal (2005), Automata Celulares (AC) são sistemas dinâmicos discretos, sendo frequentemente descritos como contrapartes às equações diferenciais parciais que apresentam a potencialidade para descrever sistemas dinâmicos contínuos. O significado de discreto é que as variáveis de estado mantêm-se inalteradas ao longo de intervalos de tempo, e mudam seus valores somente em momentos bem definidos conhecidos como passo ou tempo de ocorrência de evento. (p. 11) A ideia é procurar mostrar que a simulação de sistemas complexos ocorre por regras e interações celulares simples. Bar-Yam (1997) descreve que os Autômatos Celulares representam um dos modelos matemáticos capazes de representar sistemas e fenômenos que formam uma classe geral de modelos de sistemas dinâmicos, que são simples e ainda capturam uma rica variedade de comportamento. Isto fez deles uma ferramenta favorita para pesquisadores estudarem o comportamento genérico de sistemas dinâmicos complexos. A palavra autômato representava máquinas automáticas cujo comportamento era modelado por termos matemáticos inconfundíveis (PASCOAL, 2005). De modo especial, Neumann estava interessado com a relação dos autômatos com a Biologia ou o fenômeno biológico da auto reprodução (estudos neurofisiológicos). Stephen Wolfram, em 1983, publicou uma série de trabalhos como resultados de suas análises sobre autômato celular muito simples, mesmo com a complexidade do seu comportamento, porém induzidos por regras elementares. Ele percebeu que mecanismos similares poderiam ajudar a esclarecer fenômenos físicos complexos, o que definitivamente levou-o a publicar seu livro, em 2002. O terceiro projeto de Stephen é a Wolfram Research, é uma das empresas mais respeitadas no mundo voltada para a indústria de softwares para computação, web e nuvem, pesquisa e desenvolvimento científico. Foi fundada por ele em 1987 e possui atualmente em torno de 400 funcionários distribuídos em diferentes locais, dentre eles Illinois, Oxfordshire, Tóquio, Cambridge (MA) e Paris. Imagem 1 – Interface do site wolfram.com Fonte – www.wolfram.com Dentre os inúmeros produtos e serviços podemos destacar os dois principais projetos: o programa computacional Mathematica, carro chefe da empresa, e a Wolfram Alpha. Oferece produtos para a educação básica e superior procurando trazer o melhor do mundo da tecnologia para a educação; inúmeros produtos e serviços para dispositivos móveis; consultoria corporativa; apoio a projetos e treinamento além de manter sites e blogs atualizados sobre as empresas. O Programa computacional Mathematica existe a mais de 25 anos, lançado em 1988 é o produto original e carro chefe da empresa. Consiste
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